# Question 5919: Conjunction and Inclusive Disjunction Tables

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0010-05919 · q-20261009-advance-20261013-r05-logical-connectives-0019



## Original question and givens

Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).


- G001 — Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).





## Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.


- [mko-logical-connectives](https://ocme.evemisslab.com/en/mko/mko-logical-connectives/)





## Step-by-step derivation

S001 · impliesBefore

given8 rows A=[1, 1, 1, 0, 0, 0, 0, 0];B=[1, 1, 0, 0, 0, 0, 0, 0]

After

classical Boolean values;read all supplied rows in order0,...,7

Conditions: none

Interpret1 as True and0 as False and read all eight supplied rows.Do not assume arbitrary eight rows exhaust all valuations or prove every inference rule.Material implication is not causation.

Step identifiers and dependenciesRule: classical_eight_row_connective_scope · Uses: G001





S002 · impliesBefore

row=0;A=True;B=True

After

A∧B=True;A∨B=True

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S001





S003 · impliesBefore

row=1;A=True;B=True

After

A∧B=True;A∨B=True

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S002





S004 · impliesBefore

row=2;A=True;B=False

After

A∧B=False;A∨B=True

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S003





S005 · impliesBefore

row=3;A=False;B=False

After

A∧B=False;A∨B=False

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S004





S006 · impliesBefore

row=4;A=False;B=False

After

A∧B=False;A∨B=False

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S005





S007 · impliesBefore

row=5;A=False;B=False

After

A∧B=False;A∨B=False

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S006





S008 · impliesBefore

row=6;A=False;B=False

After

A∧B=False;A∨B=False

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S007





S009 · impliesBefore

row=7;A=False;B=False

After

A∧B=False;A∨B=False

Conditions: none

Conjunction requires both true;inclusive disjunction requires at least one true and permits both.

Step identifiers and dependenciesRule: and_inclusive_or_row · Uses: G001, S008





S010 · impliesBefore

([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])

After

complete ordered results of the two requested connectives

Conditions: none

Each output column retains all eight original rows.This checks the given classical table rowwise,not a general formal proof inferred from matching values or table labels.

Step identifiers and dependenciesRule: complete_given_connective_rows · Uses: G001, S009









## Reverse checks


- S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: de191ea937aa648302d4d6cc623b19c22b8dd104de6573a99eca07500ef04ba7
- candidate record SHA-256: 8b7225f1b4ba67cc590a30fc640e8da60632eb3b6afd4d9533efc7e6930be90e
- semantic review receipt SHA-256: 0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06f
- question-first witness SHA-256: 0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fc
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261009-advance-20261013-r05-logical-connectives-0019.json)